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arXiv:0905.0891 · Superconductor Science and Technology

A scalable readout system for a superconducting adiabatic quantum optimization system

A. J. Berkley, Mark W. Johnson, P. Bunyk, R. Harris, J Johansson, Trevor M. Lanting, E. Ladizinsky, E. Tolkacheva, M. H. S. Amin, Geordie Rose

Published Sep 13, 2010• 110 citations
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Abstract

We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling has been suppressed, thus simplifying many aspects of the readout process. The readout architecture for an $N$-qubit adiabatic quantum optimization system comprises $N$ hysteretic dc SQUIDs and $N$ rf SQUID latches controlled by $2\sqrt{N} + 2$ bias lines. The latching elements are coupled to the qubits and the dc SQUIDs are then coupled to the latching elements. This readout scheme provides two key advantages: First, the latching elements provide exceptional flux sensitivity that significantly exceeds what may be achieved by directly coupling the flux qubits to the dc SQUIDs using a practical mutual inductance. Second, the states of the latching elements are robust against the influence of ac currents generated by the switching of the hysteretic dc SQUIDs, thus allowing one to interrogate the latching elements repeatedly so as to mitigate the effects of stochastic switching of the dc SQUIDs. We demonstrate that it is possible to achieve single qubit read error rates of $<10^{-6}$ with this readout scheme. We have characterized the system-level performance of a 128-qubit readout system and have measured a readout error probability of $8\times10^{-5}$ in the presence of optimal latching element bias conditions.

DOI
10.1088/0953-2048/23/10/105014

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We have designed, fabricated and tested an XY-addressable readout system that is specifically tailored for the reading of superconducting flux qubits in an integrated circuit that could enable adiabatic quantum optimization. In such a system, the flux qubits only need to be read at the end of an adiabatic evolution when quantum mechanical tunneling has been suppressed, thus simplifying many aspects of the readout process. The readout architecture for an NNN-qubit adiabatic quantum optimization system comprises NNN hysteretic dc SQUIDs and NNN rf SQUID latches controlled by 2N+22\sqrt{N} + 22N​+2 bias lines. The latching elements are coupled to the qubits and the dc SQUIDs are then coupled to the latching elements. This readout scheme provides two key advantages: First, the latching elements provide exceptional flux sensitivity that significantly exceeds what may be achieved by directly coupling the flux qubits to the dc SQUIDs using a practical mutual inductance. Second, the states of the latching elements are robust against the influence of ac currents generated by the switching of the hysteretic dc SQUIDs, thus allowing one to interrogate the latching elements repeatedly so as to mitigate the effects of stochastic switching of the dc SQUIDs. We demonstrate that it is possible to achieve single qubit read error rates of <10−6<10^{-6}<10−6 with this readout scheme. We have characterized the system-level performance of a 128-qubit readout system and have measured a readout error probability of 8×10−58\times10^{-5}8×10−5 in the presence of optimal latching element bias conditions.
Superconducting qubits demonstrate good perspectives as scalable blocks for quantum information processing. These systems can be individually readout, addressed, and controlled, making them some of the most attractive thin-film qubits. Quantum measurements should be performed in order to readout the final state of flux qubits. To observe the dynamics of such systems, one requires a fast magnetometer with exceptional sensitivity and low back-action. We address the problem of reducing the back-action of an RF SQUID readout circuit, which may significantly destroy a Josephson flux qubit in the case of the circuits integration. The main sources of such back-action in conventional RF SQUID and DC SQUID circuits are low-ohmic shunting resistors ensuring high damping. The advantage of flux qubits is the presence of an optimal bias point at which, in the first-order approximation, the device is immune to fluctuations in readout and control lines. Nonetheless, even such systems have characteristics limited by a second-order dissipation. The dissipation can be eliminated by using an “ideal parametric readout” based on an RF SQUID acting in non-hysteretic adiabatic mode. In this paper, we propose an RF SQUID in a non-hysteretic regime as a fast, sensitive, and scalable readout system with low back-action for measurements of a single MW photon counter based on a flux qubit.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
The flux state quantum bit (qubit) is promising for a solid state implementation of scalable quantum computing. The simplest flux state qubit consists of an rf SQUID with two fluxoid states, which can be readout with a dc SQUID - the most sensitive magnetic flux detector. Efficient readout with less back-action is desirable for quantum computing. In this work, we report measurements of the switching flux and switching current distributions of under damped dc SQUIDs. The data show that single shot readout of flux qubit with very high efficiency (>99%) can be realized using underdamped hysteretic dc SQUIDs.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device (dc-SQUID). We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible.
In flux qubits, qubit states are commonly read out by a dc superconducting quantum interference device (SQUID), which is inductively coupled to the qubit and works as a persistent current detector. However, neither the bottom nor the top regions of the critical current modulation curve of the SQUID can be used for the readout. In this paper, we show that a flux-trap loop inserted to the readout SQUID provides the ability to adjust the working point, which helps to avoid this constraint. This improvement is useful for some complicated flux qubit experiments.